Problem: Find the distance between the foci of the ellipse
\[\frac{x^2}{20} + \frac{y^2}{4} = 7.\]
Solution: First, we divide both sides by 7, to get
\[\frac{x^2}{140} + \frac{y^2}{28} = 1.\]Thus, $a^2 = 140$ and $b^2 = 28,$ so $c^2 = a^2 - b^2 = 140 - 28 = 112.$  Thus, $c = \sqrt{112} = 4 \sqrt{7},$ so the distance between the foci is $2c = \boxed{8 \sqrt{7}}.$